Why the limit of the Covariance function ensures stationarity of a process?

Question

Given a Stochastic process $ x(t) $, I do not understand why the following definition of the covariance function ensures stationarity:

$ K_{xx}(\tau)=\lim_{t\to \infty}\Big( \mathbb{E}\big[ x(t+\tau)x(t)\big] - \mathbb{E}\big[x(t+\tau)\big]\mathbb{E}\big[x(t)\big]\Big ) $

Can anybody help me? I thank you in advance.